Problem: If $3x-5=10x+9$, what is $4(x+7)$?
Explanation: Subtracting $3x+9$ from both sides of the first equation gives $-14=7x$. Dividing both sides of this equation by 7 shows that $x=-2$. Substituting this value of $x$ into $4(x+7)$ gives $4(-2+7)=4(5)=\boxed{20}$.